We show that there exist constants $δ_1,δ_2>0$ such that if $G$ is an $(n,d,λ)$-graph with $λ/d\leδ_1$, then $G$ contains an induced cycle of length at least $δ_2n/d$. We further demonstrate that, up to a constant factor, this is best possible. Utilising our techniques, we derive that the number of non-isomorphic induced subgraphs of such $G$ is at least exponential in $n\log d/d$, and further demonstrate that this is tight up to a constant factor in the exponent.